%0 Journal Article
%T Nonnilpotent subsets in the Suzuki groups
%J International Journal of Group Theory
%I University of Isfahan
%Z 2251-7650
%A Zarrin, Mohammad
%D 2017
%\ 06/01/2017
%V 6
%N 2
%P 7-15
%! Nonnilpotent subsets in the Suzuki groups
%K Nilpotentlizer
%K Hypercenter of a group
%K Clique number
%K Graphs associated to groups
%R 10.22108/ijgt.2017.11176
%X Let $G$ be a group and $\mathcal{N}$ be the class of all nilpotent groups. A subset $A$ of $G$ is said to be nonnilpotent if for any two distinct elements $a$ and $b$ in $A$, $\langle a, b\rangle \not\in \mathcal{N}$. If, for any other nonnilpotent subset $B$ in $G$, $|A|\geq |B|$, then $A$ is said to be a maximal nonnilpotent subset and the cardinality of this subset (if it exists) is denoted by $\omega(\mathcal{N}_G)$. In this paper, among other results, we obtain $\omega(\mathcal{N}_{Suz(q)})$ and $\omega(\mathcal{N}_{PGL(2,q)})$, where $Suz(q)$ is the Suzuki simple group over the field with $q$ elements and $PGL(2,q)$ is the projective general linear group of degree $2$ over the finite field with $q$ elements, respectively.
%U https://ijgt.ui.ac.ir/article_11176_3a4049d20a5e0a7916fa9b1738b69f83.pdf